1. Using the \"Density of Sand Data\" below sample (different a. etermine the av

Question

1. Using the "Density of Sand Data" below sample (different a. etermine the average density and standard deviation for each mole fractions) based on the first three points and all of the points. 5%) b. Using an ANOVA, determine if there is a significant difference (alpha and all of between the means of the various samples based on the first three points the points. Explain your answer. (SiFrac) based on the c. Perform a linear regression of the data vs. Silicon fraction three points and the points. Describe the el equation and its significance. Hand in a nicely prepared the data and regression line. Include y error bars equal to the standard error. 0.48 0.51 0.54 0.45 2.428 2.408 2.399 2.387 2.429 2.409 2.400 2.388 2.429 2.409 2.400 2.388 2.429 2.409 2.400 2.388 2.430 2.410 2.401 2.389

Explanation / Answer

(a): First 3 points: mean=[2.4287,2.4087,2.3997,2.3877] Standard deviation=[0.0004725,0.0004725,0.0004725,0.0004725].

All the points: mean=[2.429,2.409,2.4,2.388]

Standard deviation=[0.000632,0.000632,0.000632,0.000632].

(b):Three points: total sum of squares=69.47835-69.4756=0.00275.

Treatment sum of squares=69.47834733-69.4756=0.002747.

Error sum of squares=0.00275-0.002747=0.000003.

All the points:total sum of squares=115.829338-115.824845=0.004493.

Treatment sum of squares=115.82933-115.824845=0.004485.

Error sum of squares=0.004493-0.004485=0.000008.

In both the cases we reject Ho.

Therefore, there is a significant difference between the means of various samples.

Source of variation degrees of freedom sum of squares mean sum of squares F-test Treatment 3 0.002747 0.000915667 2441.77866>4.07(table value at(3,8)) Error 8 0.000003 0.000000375 Total 11 0.00275

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